Energy level correlations in disordered metals: Beyond universality

Journal of Mathematical Physics

Volumn 37, Issue 10, 1996, Pages 4968-4985

  Andreev, A V ^a,c   Simons, B D ^b   Altshuler, B L ^a,c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c NEC LABORATORIES AMERICA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030523893     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531674     Document Type: Article

References (46)

1. C. E. Porter in Statistical Theories of Spectra: Fluctuations (Academic, New York, 1965).
2. D. Delande, in Proceedings of Les-Houches Summer School, Session LII, 1989, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1991).
3. Chaos in quantum physics in Ref. 2.
4. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
5. Here and henceforth we set ℏ = 1.
6. D. J. Thouless, Phys. Rep. 13, 93 (1974).
7. F. J. Dyson, J. Math. Phys. 3, 140,157,166 (1962).
8. M. L. Mehta, Random Matrices (Academic, New York, 1991).
9. F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991).
10. L. P. Gor'kov and G. M. Eliashberg, Zh. Éksp. Teor. Fiz. 48, 1407 (1965) [JETP, 21, 940].
11. L. P. Gor'kov and G. M. Eliashberg, Zh. Éksp. Teor. Fiz. 48, 1407 (1965) [JETP, 21, 940].
12. K. B. Efetov Adv. Phys. 32, 53 (1983).
13. J. J. Verbaarshot, H. A. Weidenmuller, and M. R. Zirnbauer, Phys. Rep. 129, 367 (1985).
14. O. Bohigas, M. J. Giannoni, and C. Schmidt, Phys. Rev. Lett. 52, 1 (1984).
15. G. Casati, F. Valz-Gris, and I. Guarnery, Lett. Nuovo Cimento 28, 279 (1980).
16. B. A. Muzykantskii and D. E. Khmelnitskii JETP Lett. 62, 76 (1995).
17. A. V. Andreev, O. Agam, B. D. Simons, and B. L. Altshuler, Phys. Rev. Lett. 76, 3947 (1996).
18. B. D. Simons, P. A. Lee, and B. L. Altshuler, Nucl. Phys. B 409, 487 (1993).
19. B. Sutherland, J. Math. Phys. 12, 251 (1971); Phys. Rev. A 4, 2019 (1971); 5, 1372 (1972).
20. B. Sutherland, J. Math. Phys. 12, 251 (1971); Phys. Rev. A 4, 2019 (1971); 5, 1372 (1972).
21. B. Sutherland, J. Math. Phys. 12, 251 (1971); Phys. Rev. A 4, 2019 (1971); 5, 1372 (1972).
22. F. Calogero, J. Math. Phys. 10, 2191,2197 (1969).
23. V. N. Prigodin, B. L. Altshuler, K. B. Efetov, and S. Iida, Phys. Rev. Lett. 72, 546 (1994).
24. M. V. Berry, Proc. R. Soc. London Ser. A 400, 229 (1985).
25. B. L. Altshuler and B. D. Simons, in Proceedings of Les-Houches Summer School, Session LXI, "Mesoscopic quantum physics," 1994, edited by E. Akkermans, G. Montambaux, J-L. Pichard, and J. Zinn-Justin (Elsevier Science B.V., Amsterdam, 1995).
26. B. L. Altshuler and B. I. Shklovskii, JETP 64, 127 (1986).
27. P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
28. B. L. Altshuler and A. G. Aronov, in Electron-Electron Interactions in Disordered Systems, edited by A. L. Efros and M. Pollak (North-Holland, Amsterdam, 1985), p. 1.
29. V. E. Kravtsov and A. D. Mirlin, Sov. Phys. JETP Lett. 60, 656 (1994). [Pis'ma ZhETF, 60, 645 (1994) ].
30. V. E. Kravtsov and A. D. Mirlin, Sov. Phys. JETP Lett. 60, 656 (1994). [Pis'ma ZhETF, 60, 645 (1994) ].
31. E. Bogomolny and J. Keating, preprint, 1996.
32. A. V. Andreev and B. L. Altshuler, Phys. Rev. Lett 75, 902 (1995).
33. The definition of a is related to the fact that the mean level spacing Δ is per spin polarization for the Unitary and Orthogonal ensemble, while for the Symplectic case it is one-half of this value.
34. In Ref. 28 misprints were made. We are grateful to E. Bogomolny and J. Keating for bringing this to our attention.
35. Note that the product in Eq. (10d) converges in dimension below four.
36. F. Wegner, Z. Phys. 35, 207 (1979).
37. J. J. Verbaarschot and M. R. Zirnbauer, J. Phys. 17, 1093 (1985).
38. Ya. Fyodorov, in Ref. 22.
39. A. Altland, S. Iida, and K. B. Efetov, J. Phys. A 26, 3545 (1993).
40. M. R. Zirnbauer, Nucl. Phys. B 265, 375 (1986).
41. 0 in the zero mode will diverge due to the presence of the infinitesimal imaginary part in s. Therefore, to obtain the final result it is necessary to take the limit x→0 limit in the final expressions.
42. This is a direct consequence of degeneracy of the manifold of stationary points corresponding to τ=π in the structure factor.
43. J.-L. Pichard and B. Shapiro, J. Phys. May (1994).
44. M. Moshe, H. Neunberger, and B. Shapiro, preprint RU-94-28, Technion PH-12-94, 1994.
45. O. Agam, B. L. Altshuler, and A. V. Andreev, Phys. Rev. Lett. 75, 4389 (1995).
46. A. V. Andreev, B. D. Simons, O. Agam, and B. L. Altshuler, to appear in Nucl. Phys. B (1996).